Computational Physics

15.5 Reducing critical slowing down 503 0 0.2 0.4 0.6 0.8 1 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 kBT/J Γ/ J L=8 L=12 L=20 L=30 ...

504 Computational methods for lattice field theories The geometric cluster idea has also been used for spin systems formulated o ...

15.5 Reducing critical slowing down 505 the neighbouring sites of the finer grids, after which we again perform a few MC steps, ...

506 Computational methods for lattice field theories N N' n n n' n' Figure 15.5. Two neighbouring blocks on a fine lattice with ...

15.5 Reducing critical slowing down 507 of the quadratic term is negative, whereas the coefficientgofφ^4 is positive. This means ...

508 Computational methods for lattice field theories By integrating out the momenta it is clear that an MD simulation at constan ...

15.6 Comparison of algorithms for scalar field theory 509 Updateφkusing(15.103)with time steps(15.105); FFT:φk→φn; END LangStep. ...

510 Computational methods for lattice field theories Table 15.3.Comparison between different methods for simulating the scalar q ...

15.7 Gauge field theories 511 have a more complicated structure. They include several kinds of particles, some of which are ferm ...

512 Computational methods for lattice field theories where the path integral is over all vector potential fields that are compat ...

15.7 Gauge field theories 513 Grassmann variables are anticommuting numbers – Grassmann numbersaandb have the properties: ab+ba= ...

514 Computational methods for lattice field theories nn+
n+ n+
+ Figure 15.6. A lattice plaquette at sitenwith sidesμandνused ...

15.7 Gauge field theories 515 The total action SLQED= ∑ n;μν Splaquette(n;μν) (15.125) occurs in the exponent of the time-evolut ...

516 Computational methods for lattice field theories C t x t x (a) (b) Figure 15.7. The Wilson loop on a two-dimensional square ...

15.7 Gauge field theories 517 Zis the vacuum partition function. Note that the fact thatTis taken large guarantees that the grou ...

518 Computational methods for lattice field theories of electrodynamics in which the interaction energy increases linearly with ...

15.7 Gauge field theories 519 The system can be simulated straightforwardly using the Metropolis algorithm, but we shall use the ...

520 Computational methods for lattice field theories 0.01 0.1 1 0 5 10 15 20 25 30 35 40 45 50 W(C) Area 16 × 16 32 × 32 Figure ...

15.7 Gauge field theories 521 15.7.4 Including dynamical fermions In real problems studied by particle physicists, fermions are ...

522 Computational methods for lattice field theories One could ignore the doubling problem and live with the fact that the theor ...